Question

Find the average of the function over the given interval and all values of x in the interval for which the function equals its average value. (Round your answer to three decimal places.)

f(x) = 8 cos(x),
(0, π/6)

...?

Answer 1

Integrate and then divide by the length of the path
i.e. find


`(6)/(\pi)\int_0^{(\pi)/(6)} 8 \cos(x)dx`


`(48)/(\pi)\int_0^{(\pi)/(6)} \cos(x)dx \\ \\ (48)/(\pi)sin(x)|_0^ (\pi)/(6) \\ \\ (48)/(\pi)(\sin{(\pi)/(6)}-sin(0)) \\ \\ (48)/(\pi)( (1)/(2)-0) \\ \\ (48)/(\pi)* (1)/(2) \\ \\ (24)/(\pi)`